Frequency modulation system



Feb. 25, 1941 HQ RoDER 2,233,183

FREQUENCY MODULATION SYSTEM Filed Nov. 12, 1938 2 Sheets-Sheet 1 Fig. I. CARRIER FREQUENCY POWER oscILLA'roR MODULATOR AMPLIFIER 5 FILTER AMPLIFIER SIGNAL No.l CHANNEL No.1 3

9 6 CHANNEL No.2 AMPLIFIER SIGNAL No.2 F1 5 FILTER 7 AMPLITUDE SIGNAL No.3 MODULATORS CHANNEL No.5 AMFLIF/ a FILTER OSCILLATOR OSCILLATOR suacARRIER SUBCARRIER cI-IA NEL No.8 CHANNEL No.3

CHANNEL No. I 29 SIGNAL Ivo.

Pig. 2

FIL ER 2 7 CHANNEL No. 2 RECWHER RA DID INTERMEaIm-E 26 FIIEQIIENcY 32 AMPLIFIER CONVERTER FflEQUE/VCY LIMITER SIG/VAL No.2

FREQUENCY Z5 AMPLITUDE CONVERTER FILTER osclLLAm CHANNEL NO. 3 RECTIFIER sIaNAL No. 5

FILTER FREQUENCY POWER OFCILLATOR MODULATOR AMPLIFIER y; l F. 'l 2 5' FIQS. I

.5 FILTER AMPLIFII'R SIGNAL No-I FIOIZQUENCX E m M ULATO MIX R F LTE MPL FIE SIGNAL No.2 I R A I R I OSCILLATORS 4/ 42 oscILLAToR 56 7 FILTER AMPLIF' E sIsNAL No.3 43 I R FREQUENCY 44 MIXER 48 MODULATOR Inventor H'ans Roder,

is Attorn ey.

Feb. 25, 1941. RODER 2,233,183

FREQUENCY MODULATION SYSTEM Filed NOV. 12, 1938 2 Sheets- Sheet Fig.4.

1 1 lvm. N

OSCILLATOR RAD/0 25 FREQUENCY rnzousucv R QuszvcY INTERMEDIATE AMPLITUDE AMPLITUDE zz AMPLIFIER rnsquzncv couvsm'zn FILTER LIMITER CONVERTER SIGNAL N0. 2

22 CONVERTER LIMITER FREQUENCY AMPLITUDE CONVERTER FILTER LIMITER SIG/VAL Na. 3

l2346'6 e9 IIIzlI4- Inventor: Hans RodeT,

Hls Attorney.

Patented Feb. 25, 1941 1 UNITED-STATES FREQUENCY MODULATION SYSTEM Hans Roder, Schenectady, N. Y., assignor to General Electric Company, a corporation of New York Application November 12, 1938, Serial No. 240,144

3 Claims.

' My invention relates to frequency modulation systems and more particularly to such systems in which two or more signals are transmitted on the same carrier frequency. One of 5 its objects is to obtain. optimum noise elimination in such a system.

One of the great advantages resulting from the use of frequency modulation in the transmission of radio signals is the reduction of reception of undesired noisecurrents. Thisadvantage of frequency modulation over amplitude modulation is especially pronounced if the shift in the carrier frequency be of the order of at least five times the highest frequency to be transmitted.

It has been proposed to transmit two or more signals by modulation .of a single carrier wave. This has been done by modulating a main carrier wave and one or more subcarrier waves each with a signal to, be transmitted, the modulation of the main carrier being frequency modulation, and that of the subcarriers being either amplitude or frequency modulation. The main carrier is then additionally frequency modulated with each of the modulated subcarriers. I have found that to obtain the maximum noise elimination on the subchannels so formed the frequency of the various subcarrier waves must have a definite relationship to the shift in frequency of the main carrier produced thereby.

The novel features which I believe to be characteristic of my invention are set forth with particularity in the appended claims. My invention itself, however, both as to its organization and method of operation together with further objects and advantages thereof may best be understood by reference tothe following description taken in connection with the accompanying drawings in which Figs. 1 and 2 represent a frequency modulation transmission system; Figs. 3 and 4 represent a modification thereof, and Figs. 5, 6 and 7 represent certain diagrams pertinent to the operation of the system shown in Figs. 1 to 4.

' Referring to Fig. l of the drawings I have in dicated at I therein a carrier wave oscillator the output of which is supplied to the input of a frequency modulator. The output from this frequency modulator, which is frequency modulated in accordance with certain desired signals ma be supplied to a power amplifier 3 and supplied to an antenna 4. The various signals which are to be transmitted are supplied to the system over channels 5,'6, and I. We will assume that these signals are of the various "voice or music frequencies. Si'gnal No. 1 is supplied over circuit 5, filter 8 and amplifier 9 of channel No. 1 and conductor III to the inputof the frequency modulator 2 whereby it is caused to produce a frequency'modulation of the carrier wave radiated by the. antenna.

Signal No. 2 is supplied over circuit 6 to an amplitude modulator II in which it is caused to modulate the output from a carrier wave oscillator I2 of channel No. 2. This modulator II may be assumed to produce amplitude modulations in oscillations of the frequency of the oscillator I2 and to supply such oscillations through a filter I3 and amplifier M to the circuit I0 and hence to the input of the frequency modulator 2. Hence the frequency of the carrier wave of oscillator 2 is modulated by the carrier wave generated by oscillator I2, the amplitude of which is modulated in accordance with signal No. 2.

Signal No. 3 is supplied through a channel No. 3, similar to that through which signal No. 2 i supplied and which comprises an oscillator l5, amplitude modulator l6, filter II and amplifier. I8 whereby the frequency of the carrier wave of oscillator I is further modulated by oscillations from oscillator I5, the amplitude of which are modulated in accordance with signal N0. 3. Filters 8, I3 and II are, of course, designed to transmit only the frequencies of their respective channels.

. Fig. 2 shows a receiver adapted for use in con nection with the transmitter of Fig. 1. It comprises the antenna 20 which supplies the intercepted oscillations to a radio frequency amplifier .2I, the output of which is supplied to a superheterodyne converter 22 in which it is caused to beat with oscillations produced by the local superheterodyne oscillator 23 to produce an intermediate frequency which is supplied through an intermediate frequency amplifier 24 and amplitude limiter 25 to a frequency amplitude converter. 26 whereby the frequency variations of the received carrier wave are converted to amplitude variations thereof. In this way all of the currents supplied through circuit I0 of 4 Fig, l to modulator 2 thereof are reproduced upon the conductor 21 of Fig. 2. Signal No. 1 is then supplied through band pass filter 28 to output circuit 29 of channel No. 1. Currents of the frequency of oscillator I2 together with its modulation side bands are supplied through band pass filter 30, which is similar to filter I3 of Fig. 1, to a detector or rectifier 3| whereby signal No. 2 is reproduced on output circuit 32 of channel No. 2. Oscillation of the frequency of osciliii the channels for signals No. 2 and No. 3 involve 7 frequency modulation of their respective subcarriers rather than amplitude modulation thereof. Referring to Fig. 3 the output from oscillator I is supplied to the carrier wave input of frequency modulator 2 the output of which is supplied through a power amplifier 3 to the antenna 4.

The channel of signal No. .1 is identical with that for signal No. 1 of Fig. 1 and comprises theband pass filter 8, amplifier 9, and circuit l0 leading to the signal input of the frequency modulator 2.

The carrier wave for the channels for signals No. 2 and No. 3 is supplied by an oscillator 36 the output of which is supplied to a frequency modulator 38 whereby its frequency is modulated inaccordance with signal No. 2.. The output from this frequency modulator is reduced in frequency by means of a mixer 39 in which it is caused to beat with the output of an oscillator 40 thereby to produce a lowerfrequency car-- rier wave. This lower frequency and its side bands are supplied through a band pass filter 4|, an amplifier 42 to circuit l0.

In the same way the output of oscillator 36 is supplied to a frequency modulator 43 whereby it is frequency modulated in accordance with signal No. 3. The output from this modulator is then reduced in frequency by mixer 44 in which it is causedto beat with the oscillations from an oscillator 45. The reduced carrier wave, together with its side bands is then supplied through band p sfilter '46 and amplifier 48 to circuit I 0. In this way these carrier waves, modulated in frequency by their respective signals No. 2 and No. 3,

are caused to frequency modulate the output from oscillator No. 1.

Fig. 4 shows a receiver for use in connection with the system of Fig. 3. It is identical with the receiver of Fig. 2 with theexception that the rectifier3l of 'Fig. 2 is replaced by an amplitude limiter 49 the output of which is supplied to a frequency amplitude converter 50 whereby the frequency modulated oscillations of the frequency of the output of mixer 33 are converted to amplitude variations and supplied to circuit 32. These circuits of course represent signal No. 2. In the same way the rectifier 34 of Fig. 2 is replaced by amplitude limiter St the output of which is supplied to frequency amplitude converter 52 whereby signal No. 3 is reproduced and supplied to circuit 35. v

To consider the problem of elimination of noise in the channels through which signals No. 2 and No. 3 are transmitted let us represent the instantaneous frequency of the carrier wave emitted by the transmitter of Fig. 1 by the following equation.

w=wo+A sin a1t+B(1+kz sin art) cos bt+C'(1+ka sin aatl cos ct (1) in which =21! where f is the instantaneousfrequency emitted by the systemof Fig. 1

wo'=2rlo, where I0 is the frequency of oscillator 1 A, B and C are the individual frequency shifts produced by signal No. 1 and subcarriers on which signals No. 2 and No. 3 are modulated respec- 5- tively;

or, a: and as are the respective signal frequencies;

k: and 7C: are the percentage of modulation of the two subcarriers respectively;

b and c are the frequencies of the subcarriers respectively in radians per second; and t represents time.

The instantaneous frequency of currents emitted by the transmitter of Fig. 3 may be reprel5 sented by the following equation.

w=wo+A cos a1t'+B cos(bt+Pz sin azt) +C' cos'(ct+Pa sin act) (2) in which the terms in, we, A, B, C, d1, d2, as, b, c, 20 and t are the same as above, and Pa and Pa represent the phase shifts impressed by signals No.

2 and No. 3 upon their respective subcarriers. Now let us consider the degree to which, for example,,channel No. 3 is susceptible to interfer- 25 ence produced by undesired signals, stray electromotive forces, static, and the like. To do so let us assume that channels No. 1' and No. 2 are idle, there being no signal in channel No; 1 and no signal or subcarrier in channel No. 2. Let us 30 also assume that the 'subcarrier in channel No. 3 is unmodulated. These assumptions may be made for either of the above systemsand'the following considerations-apply to both of these I systems. 1 35 The frequency emitted .by the transmitter of either Fig. 1 or Fig. 3 then-becomes w=wo+c cos ct (3) since all other terms of both Equations 1 and 2 40v drop out under the above assumed conditions. The voltage produced in the antenna of the receiver may be expressed by the following equa- Substitutingthe value of in given by Equation 3 into Equation 5 and integrating tliat equation- 50 we get Substituting this value of into Equation 4 we 55 et e,=S sin (w t+- sin cl) (6) This equation thus represents the current produced in the antenna of the receiver during existence of the above conditions.

Now let us assume that a disturbing electromative force eh also aifec-ts the receiving antenna whose amplitude is N volts and whose frequency differs from the received carrier frequency by 2'8 kilocycles. This interfering electromotive force may be expressed as follows: 7

The total electromotive force, which we will represent by er, induced in the antenna is then the vector sum 'of e; and en.

a= sin ct of Equation 6 and From the geometry of this vector diagram we find the relation I s=pt of Equation 7 sin 6 1Y Bin (01-5-5) S where 6 represents the angle between vectors eand er.

The noise currents may be assumed to have an intensity not greater than one half of the intensity of the received signal current. A received noise current of such intensity, in any ordinary amplitude modulation system would render the received signal practically unintelligible and would produce some noticeable, although not necessarily objectionable, disturbance in a frequency modulation system. It is sufiicient for the present purposes to assume that the interfering current is of intensity less than half ofthe intensity of the desired signal current.

From Fig. 5 we then see that the angle 8 can never be greater than 30 since is never greater than For angles of a less than 30 degrees we may let and cos 6=i Substituting these quantities in Equation 10, putting.

and solving for 8 we find sin (rain-fits] (n) The quantity /2 cosh-p) is always equal to or less than /2. Therefore, the bracketed term in Equation 11 may be expanded into a power series, and Equation 11 written as follows:

Substituting this quantity into Equation 13 we find %sin [2 t+ sin (ct)]+ (l4) 1 Now using the Jacobi expansion formulas for the sine terms and denoting by t 10 I the Bessel functions of order n and argument and lettin we get (see for example. Proceedings of the Institute of Radio Engineers for December 1931, pages 2149 and 2150):

a5=m sin ct+%[.h(m) sin t2.h(m) sin ct cos t +2J (m) cos 2ct sin at %[J (2m) sin 2 t-2J (2m) sin ct cos 2 t) +2J=(2m) cos 2ct sin 2 .t (15) From this expression it is seen that the angle u8 varies at a rate dependent on a number of different frequencies 0, a, ct 2cm, 2;, c22 2012 etc.

The band pass filter 33 of the receiver of Figs. 35 2 and 4 above passes only the subcarrier and its frequency spectrum which includes its upper and lower modulation side bands. Only the frequencies 0, exp, and 0:2 1. are included in this spectrum and the terms of Equation 15 containing the other of the above mentioned frequencies may be ignored.

This expression a t=m sin ctJ1(m) sin ct cos t +%J1(2m) sin ct cos 2st (16) This expression indicates the phase angle of the vector eias a function of time. In order to find the frequency variation of the vector eiwe differentiate this expression with respect to time and we get then becomes '-J1(m)[c cos t cos ctsin t sin ct] The first term of the right hand side of this equation represents the subcarrier of frequency c, the second term represents a modulation vector of this carrier having the frequency a, and the third term represents a modulation vector having the frequency 2;.

The first term of Equation 1'1 may be representei by a horizontal vector me as shown in v Fig.

The term cJ1(1n) cos at cos ct may also be represented by a horizontal vector whose maximum length is 01101:.) but which durin onecycle of frequency ,u. varies in length as the cos at. This vector is represented in Fig. 6 and denoted by the legend cJ1(m) The term Minn) sin pt sin ct can be represented by. a vertical vector whose maxim length is aJKm) but which, during one cycle of frequency n. varies in length as the sin t. This vector is denoted by 4.1mm) in Fig. 6. 1

The vector sum of the quantities (c.h(m) cos at) and (Mum) sin t) yields a new vector M showmin Fig. 6 whose end point transcribes an ellipse as shown by the dotted line in Fig. 6. The major axis of this ellipse has a length equal to 2 cJ1(m) while'the minor axis has a length of 2 41011).

Now, of course, since Equation 17 is a frequency equation the vectors ,of Fig. 6 are frequency vectors. However, since the frequency amplitude converter performs a linear translation of frequency variations to voltage variations this diagram, Fig. 6, may be taken to represent voltage vectors as well, these voltages being those which appear at the point in Fig. 2, or at point 6| in Fig. 4.

The vector resulting from the summation of carrier vector me and modulation vector M is represented by the vector W in Fig. 6.

Now, let us first consider the receiver shown in Fig. 2. Referring to Fig. 6 vector W varies in length between a maximum of (mc+cJ1(m)) and a minimum of (mccJ1(m)) and therefore is amplitude modulated by In otherwords the unmodulated subcarrier c which is produced by oscillator l5 of Fig. 1 is received at point 60 of Fig. 2 with an amplitude modulation impressed on it of frequency a and of a modulation'depth given by Expression 18 pro- X per cent duced by the received interfering electromotive forces if the interfering electromotive forces have an intensity equal to half of the intensity of the desired signal electromotive force..

Now, let us consider how the receiver of Fig.

4 responds to the voltage represented by vector W which appears at point in Fig. 4. The limiter, of course, removes any amplitude variations.

of vector W. The phase variations, however, of the vector W, constitute the variable frequency from which the signal is reproduced through ac-' tion of the frequency amplitude converter. Let us call the instantaneous angle between vector W and the vector mo, 0.

If the approximate maximum phase displacement between vector W and vector me be desig-' nated 0m then for small phase displacements Referring now to Equation 2 we note that P3 represents the phase shift impressed by signal Bin pt cos pt (21);

No. 3 upon its respective subcarrier and that P30: is the frequency shift produced on the fre quency of that subcarrier by the desired signal. The ratio a: therefore expresses the relation between the intensity of the undesired disturbance and the desired signal.

Now we note from. Expressions 18 and 22 that the interference, in either case, is proportional to the quantity J1(m) Fig; 7 shows the function J1(m) plotted against the quantity m the curve having been plotted, of -course,-from tables of Bessel functions. It will be observed from this curve that the quantity m has a number of values for which the quantity J1 (m) is zero. The quantity m is the ratio.

the subcarrier frequency. Therefore, by making Q this ratio such that the quantity J1(m) is zero the interference will be minimized. The first three values of m for which the quantity J1(m) 1S zero are:

m= 3.83 M: 7.015 m=10.17

Accordingly, if the subcarrier frequency be for example, 50 kilocycles, then interference will be minimized if the shift of the main carrier frequency be (50) (3.83) =191 kilocycles, or (50) (7.015)=351 kilocycles; or ,(50) (10.17) =508 kilocycles. For practical reasons, however, the first of these values, 191 kilocycles, would usually be chosen although the other values may be employed to advantage in minimizing noise.

In the above consideration of Equation 17 the last term thereof was ignored. This term contributes an interference component having the frequency 2 but whose amplitude is only in/the order of one-quarter of the amplitude of the component contributed by the second term. In general the noise contributed by this term is small in comparison with that contributed by the second term, and this term may safely be disregarded. The magnitude of this term may be further indicated from Bessels functions from which we find that if m be made equal to 3.83 as is above indicated to be necessary for minimum interference, then J1(2m) =.173 which when substituted in this last term and multiplied by A renders that term entirely negli-' gible.

It will be seen from the steepness of the curve of Fig. 7 near the points where it crosses the axis m that for minimization of interference in accordance with the present invention the values of m above given should be rather closely adhered to and while some deviations'therefrom may be necessary from practicalconsideration these deviations should not depart more than ten percent from the values given.

What I claim as new and desire to secure by Letters Patent of the United States is:

1. The method of signaling which comprises modulating the frequency of a. main carrier wave at a rate dependent upon the frequency of a subcarrier wave, the range of frequencies over which the frequency of the main carrier is varied being greater than the frequency of the subcarrier substantially by any one of three multiplication factors as-follows 3.83; 7.015; and 10.17.

2. The method of signaling which comprises modulating the frequency of a main carrier wave at a rate dependent upon the frequency of a subcarrier wave the range of frequencies over which the frequency of the main carrier is varied having a ratio to the frequency of the subcarrier for which J1(m) is substantially-equal to zero where Jim!) is the Bessel function, order 1, ar-

gument m, where m is the ratio of the range of variation in frequency of the main carrier to the frequency of the subcarrier.

3. In a frequency modulation system, the method of minimizing reception of extraneous noise currents which comprises modulating the frequency of a main carrier wave at a. rate dependent upon the frequency of a subcarrier wave, the range of frequencies over which the fre- 

